2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139795Let $G$ be a locally compact group, and let $A_\cb(G)$ denote the closure of $A(G)$, the Fourier algebra of $G$, in the space of completely bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that $\cstar(G)$ is residually finite-dimensional, we show that $A_\cb(G)$ is operator amenable. In particular, $A_\cb(F_2)$ is operator amenable even though $F_2$, the free group in two generators, is not an amenable group. Moreover, we show that, if $G$ is a discrete group such that $A_\cb(G)$ is operator amenable, a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$ if and only if it has an approximate identity bounded in the cb-multiplier norm.LaTeX2e; 18 pages; cleaned up a bitFunctional AnalysisOperator AlgebrasPrimary 43A22; Secondary 43A30, 46H25, 46J10, 46J40, 46L07, 47L25text